can I get some help with discrete mathematics questions. here are the questions

Question

can I get some help with discrete mathematics questions.

here are the questions I need help with.

they are problems 3 and 4.

digraph notation. c) What does the transitive closure of R specify? What name could you give it, if you considered even larger family trees including many generations? Problem 3 a) How many different equivalence relations can we define on the set A 1, 2,3)? b) How many different partial orderings can we define on the set A 11,2 c) How many different total orderings can we define on the set A = { 1,2}? Problem 4 Find the error in the "proof" of the following "theorenm. “Theorem": Let R be a relation on a set A that is symmetric and transitive. Then R is reflexive "Proof": Let a E A. Take an element b E A such that (a, b) E R. Because R is symmetric, we also have (b, a) ER. Now using the transitive property, we can conclude that (a, a) E R because (a, b) E R and (b, a) E R. 2 Enter

Explanation / Answer

3)

a)
There are totally 5 equivalance relations for the set R
R1={(1,1),(2,2),(3,3)}
R2={(1,1),(2,2),(3,3),(1,2),(2,1)}
R3={(1,1),(2,2),(3,3),(1,3),(3,1)}
R4={(1,1),(2,2),(3,3),(2,3),(3,2)}
R5={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}

Ans: 5

b) How many different partial orderings can we define on set A={1,2}?
The formula for total number of partial orders of a relation = n!
= 2! = 2

c)Number of total orders of a relation is: n(n-1)/2
= 2(1)/2 = 1

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